Global well-posedness of the 2D primitive equations with fractional horizontal dissipation

In this paper, we investigate the two-dimensional incompressible primitive equations with fractional horizontal dissipation. Specifically, we establish global well-posedness of strong solutions for arbitrarily large initial data when the dissipation exponent satisfies $\alpha \ge {\alpha }_0\approx 1.1108$. In addition, we prove global well-posedness of strong solutions for small initial data when $\alpha \in [1,{\alpha }_0)$. Notably, the smallness assumption is imposed only on the $L^{\mathrm{\infty }}$ norm of the initial vorticity.